This One may ascend His Holy Hill—may stand in the Holy Place! Did Jesus not do that? Verse 4 describes Christ's purity, His sinlessness, and now His holiness!
Evil proceeds from within to without but so does good. Just as sin proceeds from within, so does righteousness. In Psalm 51:10, David pleads with God to create a clean heart within him because he understands that from a clean heart proceed clean thoughts and thus clean conduct that will glorify God. God promises exactly this in Ezekiel 36:25-26.